I seem to be getting incorrect numerical results for the LegendreQ[n,x]
function. For example I get:
LegendreQ[-1/2,5]//N = 1.00108 -1.17142 i
so that the imaginary part is not zero. However, using the identity
(Abramowitz and Stegun 8.3.13):
LegendreQ[-1/2, x] = Sqrt[2/(x+1)] * EllipticK[Sqrt[2/(x+1)]]
The answer should be:
Sqrt[2/(5+1)]EllipticK[Sqrt[2/(5+1)]]//N
1.11187
Michael Mandelberg